Senate Majority Leader Harry Reid says Democrats will take the unprecedented step of changing filibuster rules on a party-line vote if Republicans don’t agree to a bipartisan deal this week.

Reid and Minority Leader Mitch McConnell met Tuesday on a proposal to pare back the use of the potent stalling tactic, but the Nevada Democrat then publicly threatened to change the filibuster rules with 51 votes, rather than 67 votes, if a deal can’t be reached soon, a tactic critics warn could fundamentally transform the Senate away from a body meant to protect minority party rights.

“I hope in the next 24 to 36 hours we can get something that we agree on,” Reid told reporters after lunching with Democratic senators. “If not, we will move forward on what I think needs to be done. My caucus will support me on that.”

There are 55 members of the Democratic Caucus, and younger senators in particular have pushed for action to water down the power of filibusters, which take 60 votes and days to overcome.

As part of any deal, McConnell wants to ensure he has a guaranteed number of amendments if Reid chooses to speed debate, GOP senators said Tuesday. Senators said Reid and McConnell were also weighing elements of an alternative plan led by Sens. Carl Levin (D-Mich.) and John McCain (R-Ariz.) that would guarantee Republicans at least two amendments while preventing them from filibustering in a handful of situations.

Reid is proposing a series of more modest changes that he believes would allow him to streamline the legislative process. He wants to eliminate filibusters used to prevent debate on legislation from starting. He also wants to end filibusters to prevent the Senate from entering talks with the House. And he’d like to pare back the use of filibusters on certain presidential nominations, particularly district court judicial nominees.

He’s also considering requiring 41 senators to vote to sustain a filibuster, a subtle shift from the current practice that requires 60 votes to break the stalling tactic. The proposed approach would shift the burden on the opposing party and force the opponents to ensure all their votes are present. Several Republican senators were cool on that idea on Tuesday.

Once a filibuster is defeated, the Senate immediately moves into 30 hours of debate, under current rules. Reid is now weighing whether to make senators actually hold the floor and speak for those 30 hours if they refuse to speed the debate.

Reid’s comments Tuesday show the majority leader feels he has the support from his caucus to get the 51 votes needed to change the rules without GOP support — even though many in the Democratic Caucus feel the changes do not go far enough.

That 51-vote move — dubbed by critics as the “nuclear option” — has never been successfully accomplished on the first day of a new Senate because of fears it could create a precedent exploited by future majorities to easily change rules designed to give the minority party tremendous power to block legislation.

“There’s, I think in the caucus, 51 votes to do something to the rules,” said Sen. Mark Begich (D-Alaska.). “Where we are today is unacceptable.”

But Republicans say the filibuster isn’t the problem. They say it’s Reid’s penchant for blocking off their efforts to amend legislation.

“The Senate isn’t functioning as it should,” McConnell said on the floor Tuesday. “And it has nothing to do with a process that has served us well for a very long time. But if we work together and strive to avoid some of the bad habits we’ve developed around here, I believe we’ll be able to achieve the solutions that have eluded us for the past four years.”

Tuesday morning, Reid announced he would use a procedural maneuver to extend the first legislative day of the session for potentially several more days by recessing the chamber, rather than adjourning. That would preserve his right to use the 51-vote option to change the rules — which supporters call the “constitutional option” — and give him leverage in his back-channel talks with McConnell.

The Senate will first seek to move emergency legislation providing aid for victims of Superstorm Sandy this week before debating a new rules package on the floor, Reid said.

Reid has made one concession in the talks with McConnell. He’s ready to drop a far-reaching proposal from Sens. Jeff Merkley (D-Ore.), Tom Udall (D-N.M.) and Tom Harkin (D-Iowa): the “talking filibuster,” which would end the practice of senators simply threatening a filibuster and actually make them go to the floor and carry one out, like in the classic film, “Mr. Smith Goes to Washington.”

But since the proposal would allow a filibuster to be overcome by 51 votes when the obstructing senators stop talking, a number of senators in both parties are squeamish about going down that path, fearing it would forever change the institution.